TSTP Solution File: GRP369-1 by SnakeForV-SAT---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : SnakeForV-SAT---1.0
% Problem : GRP369-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% Computer : n008.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Aug 31 16:21:27 EDT 2022
% Result : Unsatisfiable 1.55s 0.59s
% Output : Refutation 1.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 72
% Syntax : Number of formulae : 331 ( 9 unt; 0 def)
% Number of atoms : 1712 ( 398 equ)
% Maximal formula atoms : 13 ( 5 avg)
% Number of connectives : 2746 (1365 ~;1355 |; 0 &)
% ( 26 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 6 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 28 ( 26 usr; 27 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 10 con; 0-2 aty)
% Number of variables : 86 ( 86 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1033,plain,
$false,
inference(avatar_sat_refutation,[],[f64,f73,f78,f87,f96,f97,f98,f99,f104,f109,f117,f118,f119,f128,f129,f130,f131,f147,f148,f152,f153,f157,f158,f159,f160,f161,f162,f163,f164,f165,f166,f167,f168,f169,f170,f171,f172,f173,f174,f175,f176,f177,f178,f179,f183,f184,f185,f356,f372,f385,f398,f411,f424,f669,f678,f728,f832,f928,f961,f996,f1027,f1032]) ).
fof(f1032,plain,
( ~ spl4_1
| spl4_3
| ~ spl4_4
| ~ spl4_6
| ~ spl4_8
| ~ spl4_10
| ~ spl4_14 ),
inference(avatar_contradiction_clause,[],[f1031]) ).
fof(f1031,plain,
( $false
| ~ spl4_1
| spl4_3
| ~ spl4_4
| ~ spl4_6
| ~ spl4_8
| ~ spl4_10
| ~ spl4_14 ),
inference(trivial_inequality_removal,[],[f1030]) ).
fof(f1030,plain,
( identity != identity
| ~ spl4_1
| spl4_3
| ~ spl4_4
| ~ spl4_6
| ~ spl4_8
| ~ spl4_10
| ~ spl4_14 ),
inference(superposition,[],[f1029,f531]) ).
fof(f531,plain,
( identity = sk_c7
| ~ spl4_1
| ~ spl4_4
| ~ spl4_6
| ~ spl4_8
| ~ spl4_10
| ~ spl4_14 ),
inference(forward_demodulation,[],[f523,f2]) ).
fof(f2,axiom,
! [X0] : identity = multiply(inverse(X0),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_inverse) ).
fof(f523,plain,
( sk_c7 = multiply(inverse(sk_c7),sk_c7)
| ~ spl4_1
| ~ spl4_4
| ~ spl4_6
| ~ spl4_8
| ~ spl4_10
| ~ spl4_14 ),
inference(backward_demodulation,[],[f472,f499]) ).
fof(f499,plain,
( sk_c7 = sk_c9
| ~ spl4_1
| ~ spl4_4
| ~ spl4_6
| ~ spl4_8
| ~ spl4_10
| ~ spl4_14 ),
inference(backward_demodulation,[],[f458,f498]) ).
fof(f498,plain,
( sk_c7 = multiply(sk_c7,sk_c9)
| ~ spl4_6
| ~ spl4_14 ),
inference(forward_demodulation,[],[f496,f82]) ).
fof(f82,plain,
( sk_c7 = inverse(sk_c3)
| ~ spl4_6 ),
inference(avatar_component_clause,[],[f80]) ).
fof(f80,plain,
( spl4_6
<=> sk_c7 = inverse(sk_c3) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_6])]) ).
fof(f496,plain,
( sk_c7 = multiply(inverse(sk_c3),sk_c9)
| ~ spl4_14 ),
inference(superposition,[],[f198,f123]) ).
fof(f123,plain,
( sk_c9 = multiply(sk_c3,sk_c7)
| ~ spl4_14 ),
inference(avatar_component_clause,[],[f121]) ).
fof(f121,plain,
( spl4_14
<=> sk_c9 = multiply(sk_c3,sk_c7) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_14])]) ).
fof(f198,plain,
! [X2,X3] : multiply(inverse(X2),multiply(X2,X3)) = X3,
inference(forward_demodulation,[],[f191,f1]) ).
fof(f1,axiom,
! [X0] : multiply(identity,X0) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_identity) ).
fof(f191,plain,
! [X2,X3] : multiply(inverse(X2),multiply(X2,X3)) = multiply(identity,X3),
inference(superposition,[],[f3,f2]) ).
fof(f3,axiom,
! [X2,X0,X1] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity) ).
fof(f458,plain,
( sk_c9 = multiply(sk_c7,sk_c9)
| ~ spl4_1
| ~ spl4_4
| ~ spl4_8
| ~ spl4_10 ),
inference(backward_demodulation,[],[f59,f457]) ).
fof(f457,plain,
( sk_c9 = sk_c8
| ~ spl4_4
| ~ spl4_8
| ~ spl4_10 ),
inference(backward_demodulation,[],[f72,f456]) ).
fof(f456,plain,
( sk_c9 = multiply(sk_c9,sk_c2)
| ~ spl4_8
| ~ spl4_10 ),
inference(forward_demodulation,[],[f454,f91]) ).
fof(f91,plain,
( sk_c9 = inverse(sk_c1)
| ~ spl4_8 ),
inference(avatar_component_clause,[],[f89]) ).
fof(f89,plain,
( spl4_8
<=> sk_c9 = inverse(sk_c1) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_8])]) ).
fof(f454,plain,
( sk_c9 = multiply(inverse(sk_c1),sk_c2)
| ~ spl4_10 ),
inference(superposition,[],[f198,f103]) ).
fof(f103,plain,
( sk_c2 = multiply(sk_c1,sk_c9)
| ~ spl4_10 ),
inference(avatar_component_clause,[],[f101]) ).
fof(f101,plain,
( spl4_10
<=> sk_c2 = multiply(sk_c1,sk_c9) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_10])]) ).
fof(f72,plain,
( sk_c8 = multiply(sk_c9,sk_c2)
| ~ spl4_4 ),
inference(avatar_component_clause,[],[f70]) ).
fof(f70,plain,
( spl4_4
<=> sk_c8 = multiply(sk_c9,sk_c2) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_4])]) ).
fof(f59,plain,
( multiply(sk_c7,sk_c9) = sk_c8
| ~ spl4_1 ),
inference(avatar_component_clause,[],[f57]) ).
fof(f57,plain,
( spl4_1
<=> multiply(sk_c7,sk_c9) = sk_c8 ),
introduced(avatar_definition,[new_symbols(naming,[spl4_1])]) ).
fof(f472,plain,
( sk_c9 = multiply(inverse(sk_c7),sk_c9)
| ~ spl4_1
| ~ spl4_4
| ~ spl4_8
| ~ spl4_10 ),
inference(backward_demodulation,[],[f436,f457]) ).
fof(f436,plain,
( sk_c9 = multiply(inverse(sk_c7),sk_c8)
| ~ spl4_1 ),
inference(superposition,[],[f198,f59]) ).
fof(f1029,plain,
( identity != sk_c7
| ~ spl4_1
| spl4_3
| ~ spl4_4
| ~ spl4_6
| ~ spl4_8
| ~ spl4_10
| ~ spl4_14 ),
inference(forward_demodulation,[],[f1028,f751]) ).
fof(f751,plain,
identity = inverse(identity),
inference(superposition,[],[f745,f239]) ).
fof(f239,plain,
! [X1] : multiply(inverse(inverse(X1)),identity) = X1,
inference(superposition,[],[f198,f2]) ).
fof(f745,plain,
! [X3] : identity = multiply(inverse(inverse(inverse(X3))),X3),
inference(superposition,[],[f198,f239]) ).
fof(f1028,plain,
( sk_c7 != inverse(identity)
| ~ spl4_1
| spl4_3
| ~ spl4_4
| ~ spl4_6
| ~ spl4_8
| ~ spl4_10
| ~ spl4_14 ),
inference(forward_demodulation,[],[f67,f564]) ).
fof(f564,plain,
( identity = sk_c8
| ~ spl4_1
| ~ spl4_4
| ~ spl4_6
| ~ spl4_8
| ~ spl4_10
| ~ spl4_14 ),
inference(forward_demodulation,[],[f509,f531]) ).
fof(f509,plain,
( sk_c7 = sk_c8
| ~ spl4_1
| ~ spl4_4
| ~ spl4_6
| ~ spl4_8
| ~ spl4_10
| ~ spl4_14 ),
inference(backward_demodulation,[],[f457,f499]) ).
fof(f67,plain,
( sk_c7 != inverse(sk_c8)
| spl4_3 ),
inference(avatar_component_clause,[],[f66]) ).
fof(f66,plain,
( spl4_3
<=> sk_c7 = inverse(sk_c8) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_3])]) ).
fof(f1027,plain,
( ~ spl4_1
| ~ spl4_4
| ~ spl4_6
| ~ spl4_8
| ~ spl4_10
| ~ spl4_14
| ~ spl4_22 ),
inference(avatar_contradiction_clause,[],[f1026]) ).
fof(f1026,plain,
( $false
| ~ spl4_1
| ~ spl4_4
| ~ spl4_6
| ~ spl4_8
| ~ spl4_10
| ~ spl4_14
| ~ spl4_22 ),
inference(trivial_inequality_removal,[],[f1025]) ).
fof(f1025,plain,
( identity != identity
| ~ spl4_1
| ~ spl4_4
| ~ spl4_6
| ~ spl4_8
| ~ spl4_10
| ~ spl4_14
| ~ spl4_22 ),
inference(superposition,[],[f1021,f751]) ).
fof(f1021,plain,
( identity != inverse(identity)
| ~ spl4_1
| ~ spl4_4
| ~ spl4_6
| ~ spl4_8
| ~ spl4_10
| ~ spl4_14
| ~ spl4_22 ),
inference(forward_demodulation,[],[f1016,f751]) ).
fof(f1016,plain,
( identity != inverse(inverse(identity))
| ~ spl4_1
| ~ spl4_4
| ~ spl4_6
| ~ spl4_8
| ~ spl4_10
| ~ spl4_14
| ~ spl4_22 ),
inference(trivial_inequality_removal,[],[f1006]) ).
fof(f1006,plain,
( identity != inverse(inverse(identity))
| identity != identity
| ~ spl4_1
| ~ spl4_4
| ~ spl4_6
| ~ spl4_8
| ~ spl4_10
| ~ spl4_14
| ~ spl4_22 ),
inference(superposition,[],[f999,f2]) ).
fof(f999,plain,
( ! [X6] :
( identity != multiply(X6,identity)
| identity != inverse(X6) )
| ~ spl4_1
| ~ spl4_4
| ~ spl4_6
| ~ spl4_8
| ~ spl4_10
| ~ spl4_14
| ~ spl4_22 ),
inference(forward_demodulation,[],[f998,f531]) ).
fof(f998,plain,
( ! [X6] :
( sk_c7 != multiply(X6,identity)
| identity != inverse(X6) )
| ~ spl4_1
| ~ spl4_4
| ~ spl4_6
| ~ spl4_8
| ~ spl4_10
| ~ spl4_14
| ~ spl4_22 ),
inference(forward_demodulation,[],[f997,f564]) ).
fof(f997,plain,
( ! [X6] :
( sk_c7 != multiply(X6,sk_c8)
| identity != inverse(X6) )
| ~ spl4_1
| ~ spl4_4
| ~ spl4_6
| ~ spl4_8
| ~ spl4_10
| ~ spl4_14
| ~ spl4_22 ),
inference(forward_demodulation,[],[f182,f564]) ).
fof(f182,plain,
( ! [X6] :
( sk_c8 != inverse(X6)
| sk_c7 != multiply(X6,sk_c8) )
| ~ spl4_22 ),
inference(avatar_component_clause,[],[f181]) ).
fof(f181,plain,
( spl4_22
<=> ! [X6] :
( sk_c8 != inverse(X6)
| sk_c7 != multiply(X6,sk_c8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_22])]) ).
fof(f996,plain,
( ~ spl4_1
| ~ spl4_4
| ~ spl4_6
| ~ spl4_8
| ~ spl4_10
| ~ spl4_14
| ~ spl4_20 ),
inference(avatar_contradiction_clause,[],[f995]) ).
fof(f995,plain,
( $false
| ~ spl4_1
| ~ spl4_4
| ~ spl4_6
| ~ spl4_8
| ~ spl4_10
| ~ spl4_14
| ~ spl4_20 ),
inference(trivial_inequality_removal,[],[f994]) ).
fof(f994,plain,
( identity != identity
| ~ spl4_1
| ~ spl4_4
| ~ spl4_6
| ~ spl4_8
| ~ spl4_10
| ~ spl4_14
| ~ spl4_20 ),
inference(superposition,[],[f992,f751]) ).
fof(f992,plain,
( identity != inverse(identity)
| ~ spl4_1
| ~ spl4_4
| ~ spl4_6
| ~ spl4_8
| ~ spl4_10
| ~ spl4_14
| ~ spl4_20 ),
inference(forward_demodulation,[],[f991,f751]) ).
fof(f991,plain,
( identity != inverse(inverse(identity))
| ~ spl4_1
| ~ spl4_4
| ~ spl4_6
| ~ spl4_8
| ~ spl4_10
| ~ spl4_14
| ~ spl4_20 ),
inference(forward_demodulation,[],[f990,f751]) ).
fof(f990,plain,
( identity != inverse(inverse(inverse(identity)))
| ~ spl4_1
| ~ spl4_4
| ~ spl4_6
| ~ spl4_8
| ~ spl4_10
| ~ spl4_14
| ~ spl4_20 ),
inference(forward_demodulation,[],[f989,f751]) ).
fof(f989,plain,
( identity != inverse(inverse(inverse(inverse(identity))))
| ~ spl4_1
| ~ spl4_4
| ~ spl4_6
| ~ spl4_8
| ~ spl4_10
| ~ spl4_14
| ~ spl4_20 ),
inference(trivial_inequality_removal,[],[f976]) ).
fof(f976,plain,
( identity != inverse(inverse(inverse(inverse(identity))))
| identity != identity
| ~ spl4_1
| ~ spl4_4
| ~ spl4_6
| ~ spl4_8
| ~ spl4_10
| ~ spl4_14
| ~ spl4_20 ),
inference(superposition,[],[f964,f745]) ).
fof(f964,plain,
( ! [X8] :
( identity != multiply(X8,identity)
| identity != inverse(X8) )
| ~ spl4_1
| ~ spl4_4
| ~ spl4_6
| ~ spl4_8
| ~ spl4_10
| ~ spl4_14
| ~ spl4_20 ),
inference(forward_demodulation,[],[f963,f531]) ).
fof(f963,plain,
( ! [X8] :
( identity != inverse(X8)
| sk_c7 != multiply(X8,identity) )
| ~ spl4_1
| ~ spl4_4
| ~ spl4_6
| ~ spl4_8
| ~ spl4_10
| ~ spl4_14
| ~ spl4_20 ),
inference(forward_demodulation,[],[f962,f535]) ).
fof(f535,plain,
( identity = sk_c9
| ~ spl4_1
| ~ spl4_4
| ~ spl4_6
| ~ spl4_8
| ~ spl4_10
| ~ spl4_14 ),
inference(backward_demodulation,[],[f499,f531]) ).
fof(f962,plain,
( ! [X8] :
( sk_c9 != inverse(X8)
| sk_c7 != multiply(X8,identity) )
| ~ spl4_1
| ~ spl4_4
| ~ spl4_6
| ~ spl4_8
| ~ spl4_10
| ~ spl4_14
| ~ spl4_20 ),
inference(forward_demodulation,[],[f151,f535]) ).
fof(f151,plain,
( ! [X8] :
( sk_c7 != multiply(X8,sk_c9)
| sk_c9 != inverse(X8) )
| ~ spl4_20 ),
inference(avatar_component_clause,[],[f150]) ).
fof(f150,plain,
( spl4_20
<=> ! [X8] :
( sk_c9 != inverse(X8)
| sk_c7 != multiply(X8,sk_c9) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_20])]) ).
fof(f961,plain,
( ~ spl4_1
| ~ spl4_4
| ~ spl4_6
| ~ spl4_8
| ~ spl4_10
| ~ spl4_14
| ~ spl4_21 ),
inference(avatar_contradiction_clause,[],[f960]) ).
fof(f960,plain,
( $false
| ~ spl4_1
| ~ spl4_4
| ~ spl4_6
| ~ spl4_8
| ~ spl4_10
| ~ spl4_14
| ~ spl4_21 ),
inference(trivial_inequality_removal,[],[f959]) ).
fof(f959,plain,
( identity != identity
| ~ spl4_1
| ~ spl4_4
| ~ spl4_6
| ~ spl4_8
| ~ spl4_10
| ~ spl4_14
| ~ spl4_21 ),
inference(superposition,[],[f955,f751]) ).
fof(f955,plain,
( identity != inverse(identity)
| ~ spl4_1
| ~ spl4_4
| ~ spl4_6
| ~ spl4_8
| ~ spl4_10
| ~ spl4_14
| ~ spl4_21 ),
inference(forward_demodulation,[],[f954,f751]) ).
fof(f954,plain,
( identity != inverse(inverse(identity))
| ~ spl4_1
| ~ spl4_4
| ~ spl4_6
| ~ spl4_8
| ~ spl4_10
| ~ spl4_14
| ~ spl4_21 ),
inference(trivial_inequality_removal,[],[f941]) ).
fof(f941,plain,
( identity != inverse(inverse(identity))
| identity != identity
| ~ spl4_1
| ~ spl4_4
| ~ spl4_6
| ~ spl4_8
| ~ spl4_10
| ~ spl4_14
| ~ spl4_21 ),
inference(superposition,[],[f931,f2]) ).
fof(f931,plain,
( ! [X7] :
( identity != multiply(X7,identity)
| identity != inverse(X7) )
| ~ spl4_1
| ~ spl4_4
| ~ spl4_6
| ~ spl4_8
| ~ spl4_10
| ~ spl4_14
| ~ spl4_21 ),
inference(forward_demodulation,[],[f930,f535]) ).
fof(f930,plain,
( ! [X7] :
( sk_c9 != multiply(X7,identity)
| identity != inverse(X7) )
| ~ spl4_1
| ~ spl4_4
| ~ spl4_6
| ~ spl4_8
| ~ spl4_10
| ~ spl4_14
| ~ spl4_21 ),
inference(forward_demodulation,[],[f929,f564]) ).
fof(f929,plain,
( ! [X7] :
( identity != inverse(X7)
| sk_c9 != multiply(X7,sk_c8) )
| ~ spl4_1
| ~ spl4_4
| ~ spl4_6
| ~ spl4_8
| ~ spl4_10
| ~ spl4_14
| ~ spl4_21 ),
inference(forward_demodulation,[],[f156,f564]) ).
fof(f156,plain,
( ! [X7] :
( sk_c8 != inverse(X7)
| sk_c9 != multiply(X7,sk_c8) )
| ~ spl4_21 ),
inference(avatar_component_clause,[],[f155]) ).
fof(f155,plain,
( spl4_21
<=> ! [X7] :
( sk_c9 != multiply(X7,sk_c8)
| sk_c8 != inverse(X7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_21])]) ).
fof(f928,plain,
( ~ spl4_1
| ~ spl4_4
| ~ spl4_6
| ~ spl4_8
| ~ spl4_10
| ~ spl4_13
| ~ spl4_14 ),
inference(avatar_contradiction_clause,[],[f927]) ).
fof(f927,plain,
( $false
| ~ spl4_1
| ~ spl4_4
| ~ spl4_6
| ~ spl4_8
| ~ spl4_10
| ~ spl4_13
| ~ spl4_14 ),
inference(trivial_inequality_removal,[],[f926]) ).
fof(f926,plain,
( identity != identity
| ~ spl4_1
| ~ spl4_4
| ~ spl4_6
| ~ spl4_8
| ~ spl4_10
| ~ spl4_13
| ~ spl4_14 ),
inference(superposition,[],[f889,f751]) ).
fof(f889,plain,
( identity != inverse(identity)
| ~ spl4_1
| ~ spl4_4
| ~ spl4_6
| ~ spl4_8
| ~ spl4_10
| ~ spl4_13
| ~ spl4_14 ),
inference(forward_demodulation,[],[f888,f751]) ).
fof(f888,plain,
( identity != inverse(inverse(identity))
| ~ spl4_1
| ~ spl4_4
| ~ spl4_6
| ~ spl4_8
| ~ spl4_10
| ~ spl4_13
| ~ spl4_14 ),
inference(trivial_inequality_removal,[],[f876]) ).
fof(f876,plain,
( identity != identity
| identity != inverse(inverse(identity))
| ~ spl4_1
| ~ spl4_4
| ~ spl4_6
| ~ spl4_8
| ~ spl4_10
| ~ spl4_13
| ~ spl4_14 ),
inference(superposition,[],[f853,f2]) ).
fof(f853,plain,
( ! [X0] :
( identity != multiply(X0,identity)
| identity != inverse(X0) )
| ~ spl4_1
| ~ spl4_4
| ~ spl4_6
| ~ spl4_8
| ~ spl4_10
| ~ spl4_13
| ~ spl4_14 ),
inference(superposition,[],[f836,f1]) ).
fof(f836,plain,
( ! [X4] :
( identity != multiply(identity,multiply(X4,identity))
| identity != inverse(X4) )
| ~ spl4_1
| ~ spl4_4
| ~ spl4_6
| ~ spl4_8
| ~ spl4_10
| ~ spl4_13
| ~ spl4_14 ),
inference(forward_demodulation,[],[f835,f564]) ).
fof(f835,plain,
( ! [X4] :
( identity != inverse(X4)
| sk_c8 != multiply(identity,multiply(X4,identity)) )
| ~ spl4_1
| ~ spl4_4
| ~ spl4_6
| ~ spl4_8
| ~ spl4_10
| ~ spl4_13
| ~ spl4_14 ),
inference(forward_demodulation,[],[f834,f535]) ).
fof(f834,plain,
( ! [X4] :
( identity != inverse(X4)
| sk_c8 != multiply(sk_c9,multiply(X4,sk_c9)) )
| ~ spl4_1
| ~ spl4_4
| ~ spl4_6
| ~ spl4_8
| ~ spl4_10
| ~ spl4_13
| ~ spl4_14 ),
inference(forward_demodulation,[],[f116,f535]) ).
fof(f116,plain,
( ! [X4] :
( sk_c9 != inverse(X4)
| sk_c8 != multiply(sk_c9,multiply(X4,sk_c9)) )
| ~ spl4_13 ),
inference(avatar_component_clause,[],[f115]) ).
fof(f115,plain,
( spl4_13
<=> ! [X4] :
( sk_c9 != inverse(X4)
| sk_c8 != multiply(sk_c9,multiply(X4,sk_c9)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_13])]) ).
fof(f832,plain,
( ~ spl4_1
| ~ spl4_4
| ~ spl4_6
| ~ spl4_8
| ~ spl4_10
| ~ spl4_14
| ~ spl4_19 ),
inference(avatar_contradiction_clause,[],[f831]) ).
fof(f831,plain,
( $false
| ~ spl4_1
| ~ spl4_4
| ~ spl4_6
| ~ spl4_8
| ~ spl4_10
| ~ spl4_14
| ~ spl4_19 ),
inference(trivial_inequality_removal,[],[f826]) ).
fof(f826,plain,
( identity != identity
| ~ spl4_1
| ~ spl4_4
| ~ spl4_6
| ~ spl4_8
| ~ spl4_10
| ~ spl4_14
| ~ spl4_19 ),
inference(superposition,[],[f813,f751]) ).
fof(f813,plain,
( identity != inverse(identity)
| ~ spl4_1
| ~ spl4_4
| ~ spl4_6
| ~ spl4_8
| ~ spl4_10
| ~ spl4_14
| ~ spl4_19 ),
inference(trivial_inequality_removal,[],[f804]) ).
fof(f804,plain,
( identity != identity
| identity != inverse(identity)
| ~ spl4_1
| ~ spl4_4
| ~ spl4_6
| ~ spl4_8
| ~ spl4_10
| ~ spl4_14
| ~ spl4_19 ),
inference(superposition,[],[f786,f1]) ).
fof(f786,plain,
( ! [X5] :
( identity != multiply(X5,identity)
| identity != inverse(X5) )
| ~ spl4_1
| ~ spl4_4
| ~ spl4_6
| ~ spl4_8
| ~ spl4_10
| ~ spl4_14
| ~ spl4_19 ),
inference(forward_demodulation,[],[f785,f535]) ).
fof(f785,plain,
( ! [X5] :
( sk_c9 != multiply(X5,identity)
| identity != inverse(X5) )
| ~ spl4_1
| ~ spl4_4
| ~ spl4_6
| ~ spl4_8
| ~ spl4_10
| ~ spl4_14
| ~ spl4_19 ),
inference(forward_demodulation,[],[f784,f531]) ).
fof(f784,plain,
( ! [X5] :
( sk_c7 != inverse(X5)
| sk_c9 != multiply(X5,identity) )
| ~ spl4_1
| ~ spl4_4
| ~ spl4_6
| ~ spl4_8
| ~ spl4_10
| ~ spl4_14
| ~ spl4_19 ),
inference(forward_demodulation,[],[f146,f531]) ).
fof(f146,plain,
( ! [X5] :
( sk_c9 != multiply(X5,sk_c7)
| sk_c7 != inverse(X5) )
| ~ spl4_19 ),
inference(avatar_component_clause,[],[f145]) ).
fof(f145,plain,
( spl4_19
<=> ! [X5] :
( sk_c9 != multiply(X5,sk_c7)
| sk_c7 != inverse(X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_19])]) ).
fof(f728,plain,
( ~ spl4_1
| ~ spl4_4
| ~ spl4_6
| ~ spl4_7
| ~ spl4_8
| spl4_9
| ~ spl4_10
| ~ spl4_14 ),
inference(avatar_contradiction_clause,[],[f727]) ).
fof(f727,plain,
( $false
| ~ spl4_1
| ~ spl4_4
| ~ spl4_6
| ~ spl4_7
| ~ spl4_8
| spl4_9
| ~ spl4_10
| ~ spl4_14 ),
inference(trivial_inequality_removal,[],[f726]) ).
fof(f726,plain,
( identity != identity
| ~ spl4_1
| ~ spl4_4
| ~ spl4_6
| ~ spl4_7
| ~ spl4_8
| spl4_9
| ~ spl4_10
| ~ spl4_14 ),
inference(superposition,[],[f701,f1]) ).
fof(f701,plain,
( identity != multiply(identity,identity)
| ~ spl4_1
| ~ spl4_4
| ~ spl4_6
| ~ spl4_7
| ~ spl4_8
| spl4_9
| ~ spl4_10
| ~ spl4_14 ),
inference(backward_demodulation,[],[f680,f693]) ).
fof(f693,plain,
( identity = sk_c5
| ~ spl4_1
| ~ spl4_4
| ~ spl4_6
| ~ spl4_7
| ~ spl4_8
| ~ spl4_10
| ~ spl4_14 ),
inference(superposition,[],[f1,f544]) ).
fof(f544,plain,
( identity = multiply(identity,sk_c5)
| ~ spl4_1
| ~ spl4_4
| ~ spl4_6
| ~ spl4_7
| ~ spl4_8
| ~ spl4_10
| ~ spl4_14 ),
inference(forward_demodulation,[],[f516,f531]) ).
fof(f516,plain,
( identity = multiply(sk_c7,sk_c5)
| ~ spl4_1
| ~ spl4_4
| ~ spl4_6
| ~ spl4_7
| ~ spl4_8
| ~ spl4_10
| ~ spl4_14 ),
inference(backward_demodulation,[],[f465,f499]) ).
fof(f465,plain,
( identity = multiply(sk_c9,sk_c5)
| ~ spl4_4
| ~ spl4_7
| ~ spl4_8
| ~ spl4_10 ),
inference(backward_demodulation,[],[f188,f457]) ).
fof(f188,plain,
( identity = multiply(sk_c8,sk_c5)
| ~ spl4_7 ),
inference(superposition,[],[f2,f86]) ).
fof(f86,plain,
( sk_c8 = inverse(sk_c5)
| ~ spl4_7 ),
inference(avatar_component_clause,[],[f84]) ).
fof(f84,plain,
( spl4_7
<=> sk_c8 = inverse(sk_c5) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_7])]) ).
fof(f680,plain,
( identity != multiply(sk_c5,identity)
| ~ spl4_1
| ~ spl4_4
| ~ spl4_6
| ~ spl4_8
| spl4_9
| ~ spl4_10
| ~ spl4_14 ),
inference(forward_demodulation,[],[f679,f535]) ).
fof(f679,plain,
( sk_c9 != multiply(sk_c5,identity)
| ~ spl4_1
| ~ spl4_4
| ~ spl4_6
| ~ spl4_8
| spl4_9
| ~ spl4_10
| ~ spl4_14 ),
inference(forward_demodulation,[],[f94,f564]) ).
fof(f94,plain,
( sk_c9 != multiply(sk_c5,sk_c8)
| spl4_9 ),
inference(avatar_component_clause,[],[f93]) ).
fof(f93,plain,
( spl4_9
<=> sk_c9 = multiply(sk_c5,sk_c8) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_9])]) ).
fof(f678,plain,
( ~ spl4_1
| ~ spl4_4
| spl4_5
| ~ spl4_6
| ~ spl4_8
| ~ spl4_10
| ~ spl4_14
| ~ spl4_15 ),
inference(avatar_contradiction_clause,[],[f677]) ).
fof(f677,plain,
( $false
| ~ spl4_1
| ~ spl4_4
| spl4_5
| ~ spl4_6
| ~ spl4_8
| ~ spl4_10
| ~ spl4_14
| ~ spl4_15 ),
inference(trivial_inequality_removal,[],[f676]) ).
fof(f676,plain,
( identity != identity
| ~ spl4_1
| ~ spl4_4
| spl4_5
| ~ spl4_6
| ~ spl4_8
| ~ spl4_10
| ~ spl4_14
| ~ spl4_15 ),
inference(superposition,[],[f672,f531]) ).
fof(f672,plain,
( identity != sk_c7
| ~ spl4_1
| ~ spl4_4
| spl4_5
| ~ spl4_6
| ~ spl4_8
| ~ spl4_10
| ~ spl4_14
| ~ spl4_15 ),
inference(forward_demodulation,[],[f671,f1]) ).
fof(f671,plain,
( sk_c7 != multiply(identity,identity)
| ~ spl4_1
| ~ spl4_4
| spl4_5
| ~ spl4_6
| ~ spl4_8
| ~ spl4_10
| ~ spl4_14
| ~ spl4_15 ),
inference(forward_demodulation,[],[f670,f555]) ).
fof(f555,plain,
( identity = sk_c4
| ~ spl4_1
| ~ spl4_4
| ~ spl4_6
| ~ spl4_8
| ~ spl4_10
| ~ spl4_14
| ~ spl4_15 ),
inference(forward_demodulation,[],[f554,f2]) ).
fof(f554,plain,
( sk_c4 = multiply(inverse(identity),identity)
| ~ spl4_1
| ~ spl4_4
| ~ spl4_6
| ~ spl4_8
| ~ spl4_10
| ~ spl4_14
| ~ spl4_15 ),
inference(forward_demodulation,[],[f521,f531]) ).
fof(f521,plain,
( sk_c4 = multiply(inverse(sk_c7),identity)
| ~ spl4_1
| ~ spl4_4
| ~ spl4_6
| ~ spl4_8
| ~ spl4_10
| ~ spl4_14
| ~ spl4_15 ),
inference(backward_demodulation,[],[f470,f499]) ).
fof(f470,plain,
( sk_c4 = multiply(inverse(sk_c9),identity)
| ~ spl4_4
| ~ spl4_8
| ~ spl4_10
| ~ spl4_15 ),
inference(backward_demodulation,[],[f248,f457]) ).
fof(f248,plain,
( sk_c4 = multiply(inverse(sk_c8),identity)
| ~ spl4_15 ),
inference(superposition,[],[f198,f187]) ).
fof(f187,plain,
( identity = multiply(sk_c8,sk_c4)
| ~ spl4_15 ),
inference(superposition,[],[f2,f127]) ).
fof(f127,plain,
( sk_c8 = inverse(sk_c4)
| ~ spl4_15 ),
inference(avatar_component_clause,[],[f125]) ).
fof(f125,plain,
( spl4_15
<=> sk_c8 = inverse(sk_c4) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_15])]) ).
fof(f670,plain,
( sk_c7 != multiply(sk_c4,identity)
| ~ spl4_1
| ~ spl4_4
| spl4_5
| ~ spl4_6
| ~ spl4_8
| ~ spl4_10
| ~ spl4_14 ),
inference(forward_demodulation,[],[f76,f564]) ).
fof(f76,plain,
( sk_c7 != multiply(sk_c4,sk_c8)
| spl4_5 ),
inference(avatar_component_clause,[],[f75]) ).
fof(f75,plain,
( spl4_5
<=> sk_c7 = multiply(sk_c4,sk_c8) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_5])]) ).
fof(f669,plain,
( ~ spl4_1
| ~ spl4_2
| ~ spl4_4
| ~ spl4_6
| ~ spl4_8
| ~ spl4_10
| spl4_11
| ~ spl4_14 ),
inference(avatar_contradiction_clause,[],[f668]) ).
fof(f668,plain,
( $false
| ~ spl4_1
| ~ spl4_2
| ~ spl4_4
| ~ spl4_6
| ~ spl4_8
| ~ spl4_10
| spl4_11
| ~ spl4_14 ),
inference(trivial_inequality_removal,[],[f667]) ).
fof(f667,plain,
( identity != identity
| ~ spl4_1
| ~ spl4_2
| ~ spl4_4
| ~ spl4_6
| ~ spl4_8
| ~ spl4_10
| spl4_11
| ~ spl4_14 ),
inference(superposition,[],[f654,f1]) ).
fof(f654,plain,
( identity != multiply(identity,identity)
| ~ spl4_1
| ~ spl4_2
| ~ spl4_4
| ~ spl4_6
| ~ spl4_8
| ~ spl4_10
| spl4_11
| ~ spl4_14 ),
inference(backward_demodulation,[],[f606,f650]) ).
fof(f650,plain,
( identity = sk_c6
| ~ spl4_1
| ~ spl4_2
| ~ spl4_4
| ~ spl4_6
| ~ spl4_8
| ~ spl4_10
| ~ spl4_14 ),
inference(superposition,[],[f1,f536]) ).
fof(f536,plain,
( identity = multiply(identity,sk_c6)
| ~ spl4_1
| ~ spl4_2
| ~ spl4_4
| ~ spl4_6
| ~ spl4_8
| ~ spl4_10
| ~ spl4_14 ),
inference(backward_demodulation,[],[f504,f531]) ).
fof(f504,plain,
( identity = multiply(sk_c7,sk_c6)
| ~ spl4_1
| ~ spl4_2
| ~ spl4_4
| ~ spl4_6
| ~ spl4_8
| ~ spl4_10
| ~ spl4_14 ),
inference(backward_demodulation,[],[f189,f499]) ).
fof(f189,plain,
( identity = multiply(sk_c9,sk_c6)
| ~ spl4_2 ),
inference(superposition,[],[f2,f63]) ).
fof(f63,plain,
( sk_c9 = inverse(sk_c6)
| ~ spl4_2 ),
inference(avatar_component_clause,[],[f61]) ).
fof(f61,plain,
( spl4_2
<=> sk_c9 = inverse(sk_c6) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_2])]) ).
fof(f606,plain,
( identity != multiply(sk_c6,identity)
| ~ spl4_1
| ~ spl4_4
| ~ spl4_6
| ~ spl4_8
| ~ spl4_10
| spl4_11
| ~ spl4_14 ),
inference(forward_demodulation,[],[f605,f531]) ).
fof(f605,plain,
( sk_c7 != multiply(sk_c6,identity)
| ~ spl4_1
| ~ spl4_4
| ~ spl4_6
| ~ spl4_8
| ~ spl4_10
| spl4_11
| ~ spl4_14 ),
inference(forward_demodulation,[],[f107,f535]) ).
fof(f107,plain,
( sk_c7 != multiply(sk_c6,sk_c9)
| spl4_11 ),
inference(avatar_component_clause,[],[f106]) ).
fof(f106,plain,
( spl4_11
<=> sk_c7 = multiply(sk_c6,sk_c9) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_11])]) ).
fof(f424,plain,
( ~ spl4_2
| ~ spl4_3
| ~ spl4_5
| ~ spl4_7
| ~ spl4_9
| ~ spl4_11
| ~ spl4_15
| ~ spl4_22 ),
inference(avatar_contradiction_clause,[],[f423]) ).
fof(f423,plain,
( $false
| ~ spl4_2
| ~ spl4_3
| ~ spl4_5
| ~ spl4_7
| ~ spl4_9
| ~ spl4_11
| ~ spl4_15
| ~ spl4_22 ),
inference(trivial_inequality_removal,[],[f422]) ).
fof(f422,plain,
( identity != identity
| ~ spl4_2
| ~ spl4_3
| ~ spl4_5
| ~ spl4_7
| ~ spl4_9
| ~ spl4_11
| ~ spl4_15
| ~ spl4_22 ),
inference(superposition,[],[f420,f297]) ).
fof(f297,plain,
( identity = inverse(identity)
| ~ spl4_2
| ~ spl4_3
| ~ spl4_5
| ~ spl4_7
| ~ spl4_9
| ~ spl4_11
| ~ spl4_15 ),
inference(forward_demodulation,[],[f265,f277]) ).
fof(f277,plain,
( identity = sk_c7
| ~ spl4_2
| ~ spl4_3
| ~ spl4_5
| ~ spl4_7
| ~ spl4_9
| ~ spl4_11
| ~ spl4_15 ),
inference(backward_demodulation,[],[f231,f268]) ).
fof(f268,plain,
( identity = multiply(sk_c7,sk_c7)
| ~ spl4_2
| ~ spl4_3
| ~ spl4_5
| ~ spl4_7
| ~ spl4_9
| ~ spl4_11
| ~ spl4_15 ),
inference(backward_demodulation,[],[f186,f264]) ).
fof(f264,plain,
( sk_c7 = sk_c8
| ~ spl4_2
| ~ spl4_3
| ~ spl4_5
| ~ spl4_7
| ~ spl4_9
| ~ spl4_11
| ~ spl4_15 ),
inference(backward_demodulation,[],[f255,f261]) ).
fof(f261,plain,
( sk_c7 = multiply(sk_c8,sk_c7)
| ~ spl4_2
| ~ spl4_3
| ~ spl4_5
| ~ spl4_7
| ~ spl4_9
| ~ spl4_11
| ~ spl4_15 ),
inference(backward_demodulation,[],[f219,f259]) ).
fof(f259,plain,
( sk_c8 = sk_c6
| ~ spl4_2
| ~ spl4_3
| ~ spl4_5
| ~ spl4_7
| ~ spl4_9
| ~ spl4_15 ),
inference(backward_demodulation,[],[f249,f247]) ).
fof(f247,plain,
( sk_c8 = multiply(inverse(sk_c7),identity)
| ~ spl4_3 ),
inference(superposition,[],[f198,f186]) ).
fof(f249,plain,
( sk_c6 = multiply(inverse(sk_c7),identity)
| ~ spl4_2
| ~ spl4_3
| ~ spl4_5
| ~ spl4_7
| ~ spl4_9
| ~ spl4_15 ),
inference(superposition,[],[f198,f220]) ).
fof(f220,plain,
( identity = multiply(sk_c7,sk_c6)
| ~ spl4_2
| ~ spl4_3
| ~ spl4_5
| ~ spl4_7
| ~ spl4_9
| ~ spl4_15 ),
inference(backward_demodulation,[],[f189,f216]) ).
fof(f216,plain,
( sk_c7 = sk_c9
| ~ spl4_3
| ~ spl4_5
| ~ spl4_7
| ~ spl4_9
| ~ spl4_15 ),
inference(forward_demodulation,[],[f214,f77]) ).
fof(f77,plain,
( sk_c7 = multiply(sk_c4,sk_c8)
| ~ spl4_5 ),
inference(avatar_component_clause,[],[f75]) ).
fof(f214,plain,
( sk_c9 = multiply(sk_c4,sk_c8)
| ~ spl4_3
| ~ spl4_7
| ~ spl4_9
| ~ spl4_15 ),
inference(backward_demodulation,[],[f95,f210]) ).
fof(f210,plain,
( sk_c4 = sk_c5
| ~ spl4_3
| ~ spl4_7
| ~ spl4_15 ),
inference(forward_demodulation,[],[f207,f206]) ).
fof(f206,plain,
( sk_c4 = multiply(sk_c7,identity)
| ~ spl4_3
| ~ spl4_15 ),
inference(superposition,[],[f199,f187]) ).
fof(f199,plain,
( ! [X11] : multiply(sk_c7,multiply(sk_c8,X11)) = X11
| ~ spl4_3 ),
inference(forward_demodulation,[],[f196,f1]) ).
fof(f196,plain,
( ! [X11] : multiply(sk_c7,multiply(sk_c8,X11)) = multiply(identity,X11)
| ~ spl4_3 ),
inference(superposition,[],[f3,f186]) ).
fof(f207,plain,
( sk_c5 = multiply(sk_c7,identity)
| ~ spl4_3
| ~ spl4_7 ),
inference(superposition,[],[f199,f188]) ).
fof(f95,plain,
( sk_c9 = multiply(sk_c5,sk_c8)
| ~ spl4_9 ),
inference(avatar_component_clause,[],[f93]) ).
fof(f219,plain,
( sk_c7 = multiply(sk_c6,sk_c7)
| ~ spl4_3
| ~ spl4_5
| ~ spl4_7
| ~ spl4_9
| ~ spl4_11
| ~ spl4_15 ),
inference(backward_demodulation,[],[f108,f216]) ).
fof(f108,plain,
( sk_c7 = multiply(sk_c6,sk_c9)
| ~ spl4_11 ),
inference(avatar_component_clause,[],[f106]) ).
fof(f255,plain,
( sk_c8 = multiply(sk_c8,sk_c7)
| ~ spl4_5
| ~ spl4_15 ),
inference(forward_demodulation,[],[f246,f127]) ).
fof(f246,plain,
( sk_c8 = multiply(inverse(sk_c4),sk_c7)
| ~ spl4_5 ),
inference(superposition,[],[f198,f77]) ).
fof(f186,plain,
( identity = multiply(sk_c7,sk_c8)
| ~ spl4_3 ),
inference(superposition,[],[f2,f68]) ).
fof(f68,plain,
( sk_c7 = inverse(sk_c8)
| ~ spl4_3 ),
inference(avatar_component_clause,[],[f66]) ).
fof(f231,plain,
( sk_c7 = multiply(sk_c7,sk_c7)
| ~ spl4_2
| ~ spl4_3
| ~ spl4_5
| ~ spl4_7
| ~ spl4_9
| ~ spl4_11
| ~ spl4_15 ),
inference(superposition,[],[f222,f219]) ).
fof(f222,plain,
( ! [X0] : multiply(sk_c7,multiply(sk_c6,X0)) = X0
| ~ spl4_2
| ~ spl4_3
| ~ spl4_5
| ~ spl4_7
| ~ spl4_9
| ~ spl4_15 ),
inference(backward_demodulation,[],[f205,f216]) ).
fof(f205,plain,
( ! [X0] : multiply(sk_c9,multiply(sk_c6,X0)) = X0
| ~ spl4_2 ),
inference(forward_demodulation,[],[f204,f1]) ).
fof(f204,plain,
( ! [X0] : multiply(identity,X0) = multiply(sk_c9,multiply(sk_c6,X0))
| ~ spl4_2 ),
inference(superposition,[],[f3,f189]) ).
fof(f265,plain,
( sk_c7 = inverse(sk_c7)
| ~ spl4_2
| ~ spl4_3
| ~ spl4_5
| ~ spl4_7
| ~ spl4_9
| ~ spl4_11
| ~ spl4_15 ),
inference(backward_demodulation,[],[f68,f264]) ).
fof(f420,plain,
( identity != inverse(identity)
| ~ spl4_2
| ~ spl4_3
| ~ spl4_5
| ~ spl4_7
| ~ spl4_9
| ~ spl4_11
| ~ spl4_15
| ~ spl4_22 ),
inference(trivial_inequality_removal,[],[f415]) ).
fof(f415,plain,
( identity != identity
| identity != inverse(identity)
| ~ spl4_2
| ~ spl4_3
| ~ spl4_5
| ~ spl4_7
| ~ spl4_9
| ~ spl4_11
| ~ spl4_15
| ~ spl4_22 ),
inference(superposition,[],[f414,f1]) ).
fof(f414,plain,
( ! [X6] :
( identity != multiply(X6,identity)
| identity != inverse(X6) )
| ~ spl4_2
| ~ spl4_3
| ~ spl4_5
| ~ spl4_7
| ~ spl4_9
| ~ spl4_11
| ~ spl4_15
| ~ spl4_22 ),
inference(forward_demodulation,[],[f413,f277]) ).
fof(f413,plain,
( ! [X6] :
( identity != inverse(X6)
| sk_c7 != multiply(X6,identity) )
| ~ spl4_2
| ~ spl4_3
| ~ spl4_5
| ~ spl4_7
| ~ spl4_9
| ~ spl4_11
| ~ spl4_15
| ~ spl4_22 ),
inference(forward_demodulation,[],[f412,f283]) ).
fof(f283,plain,
( identity = sk_c8
| ~ spl4_2
| ~ spl4_3
| ~ spl4_5
| ~ spl4_7
| ~ spl4_9
| ~ spl4_11
| ~ spl4_15 ),
inference(backward_demodulation,[],[f264,f277]) ).
fof(f412,plain,
( ! [X6] :
( sk_c8 != inverse(X6)
| sk_c7 != multiply(X6,identity) )
| ~ spl4_2
| ~ spl4_3
| ~ spl4_5
| ~ spl4_7
| ~ spl4_9
| ~ spl4_11
| ~ spl4_15
| ~ spl4_22 ),
inference(forward_demodulation,[],[f182,f283]) ).
fof(f411,plain,
( ~ spl4_2
| ~ spl4_3
| ~ spl4_5
| ~ spl4_7
| ~ spl4_9
| ~ spl4_11
| ~ spl4_15
| ~ spl4_21 ),
inference(avatar_contradiction_clause,[],[f410]) ).
fof(f410,plain,
( $false
| ~ spl4_2
| ~ spl4_3
| ~ spl4_5
| ~ spl4_7
| ~ spl4_9
| ~ spl4_11
| ~ spl4_15
| ~ spl4_21 ),
inference(trivial_inequality_removal,[],[f409]) ).
fof(f409,plain,
( identity != identity
| ~ spl4_2
| ~ spl4_3
| ~ spl4_5
| ~ spl4_7
| ~ spl4_9
| ~ spl4_11
| ~ spl4_15
| ~ spl4_21 ),
inference(superposition,[],[f408,f297]) ).
fof(f408,plain,
( identity != inverse(identity)
| ~ spl4_2
| ~ spl4_3
| ~ spl4_5
| ~ spl4_7
| ~ spl4_9
| ~ spl4_11
| ~ spl4_15
| ~ spl4_21 ),
inference(forward_demodulation,[],[f407,f297]) ).
fof(f407,plain,
( identity != inverse(inverse(identity))
| ~ spl4_2
| ~ spl4_3
| ~ spl4_5
| ~ spl4_7
| ~ spl4_9
| ~ spl4_11
| ~ spl4_15
| ~ spl4_21 ),
inference(trivial_inequality_removal,[],[f403]) ).
fof(f403,plain,
( identity != inverse(inverse(identity))
| identity != identity
| ~ spl4_2
| ~ spl4_3
| ~ spl4_5
| ~ spl4_7
| ~ spl4_9
| ~ spl4_11
| ~ spl4_15
| ~ spl4_21 ),
inference(superposition,[],[f401,f2]) ).
fof(f401,plain,
( ! [X7] :
( identity != multiply(X7,identity)
| identity != inverse(X7) )
| ~ spl4_2
| ~ spl4_3
| ~ spl4_5
| ~ spl4_7
| ~ spl4_9
| ~ spl4_11
| ~ spl4_15
| ~ spl4_21 ),
inference(forward_demodulation,[],[f400,f283]) ).
fof(f400,plain,
( ! [X7] :
( identity != multiply(X7,identity)
| sk_c8 != inverse(X7) )
| ~ spl4_2
| ~ spl4_3
| ~ spl4_5
| ~ spl4_7
| ~ spl4_9
| ~ spl4_11
| ~ spl4_15
| ~ spl4_21 ),
inference(forward_demodulation,[],[f399,f279]) ).
fof(f279,plain,
( identity = sk_c9
| ~ spl4_2
| ~ spl4_3
| ~ spl4_5
| ~ spl4_7
| ~ spl4_9
| ~ spl4_11
| ~ spl4_15 ),
inference(backward_demodulation,[],[f216,f277]) ).
fof(f399,plain,
( ! [X7] :
( sk_c9 != multiply(X7,identity)
| sk_c8 != inverse(X7) )
| ~ spl4_2
| ~ spl4_3
| ~ spl4_5
| ~ spl4_7
| ~ spl4_9
| ~ spl4_11
| ~ spl4_15
| ~ spl4_21 ),
inference(forward_demodulation,[],[f156,f283]) ).
fof(f398,plain,
( ~ spl4_2
| ~ spl4_3
| ~ spl4_5
| ~ spl4_7
| ~ spl4_9
| ~ spl4_11
| ~ spl4_15
| ~ spl4_20 ),
inference(avatar_contradiction_clause,[],[f397]) ).
fof(f397,plain,
( $false
| ~ spl4_2
| ~ spl4_3
| ~ spl4_5
| ~ spl4_7
| ~ spl4_9
| ~ spl4_11
| ~ spl4_15
| ~ spl4_20 ),
inference(trivial_inequality_removal,[],[f396]) ).
fof(f396,plain,
( identity != identity
| ~ spl4_2
| ~ spl4_3
| ~ spl4_5
| ~ spl4_7
| ~ spl4_9
| ~ spl4_11
| ~ spl4_15
| ~ spl4_20 ),
inference(superposition,[],[f394,f297]) ).
fof(f394,plain,
( identity != inverse(identity)
| ~ spl4_2
| ~ spl4_3
| ~ spl4_5
| ~ spl4_7
| ~ spl4_9
| ~ spl4_11
| ~ spl4_15
| ~ spl4_20 ),
inference(trivial_inequality_removal,[],[f389]) ).
fof(f389,plain,
( identity != identity
| identity != inverse(identity)
| ~ spl4_2
| ~ spl4_3
| ~ spl4_5
| ~ spl4_7
| ~ spl4_9
| ~ spl4_11
| ~ spl4_15
| ~ spl4_20 ),
inference(superposition,[],[f388,f1]) ).
fof(f388,plain,
( ! [X8] :
( identity != multiply(X8,identity)
| identity != inverse(X8) )
| ~ spl4_2
| ~ spl4_3
| ~ spl4_5
| ~ spl4_7
| ~ spl4_9
| ~ spl4_11
| ~ spl4_15
| ~ spl4_20 ),
inference(forward_demodulation,[],[f387,f277]) ).
fof(f387,plain,
( ! [X8] :
( sk_c7 != multiply(X8,identity)
| identity != inverse(X8) )
| ~ spl4_2
| ~ spl4_3
| ~ spl4_5
| ~ spl4_7
| ~ spl4_9
| ~ spl4_11
| ~ spl4_15
| ~ spl4_20 ),
inference(forward_demodulation,[],[f386,f279]) ).
fof(f386,plain,
( ! [X8] :
( sk_c9 != inverse(X8)
| sk_c7 != multiply(X8,identity) )
| ~ spl4_2
| ~ spl4_3
| ~ spl4_5
| ~ spl4_7
| ~ spl4_9
| ~ spl4_11
| ~ spl4_15
| ~ spl4_20 ),
inference(forward_demodulation,[],[f151,f279]) ).
fof(f385,plain,
( ~ spl4_2
| ~ spl4_3
| ~ spl4_5
| ~ spl4_7
| ~ spl4_9
| ~ spl4_11
| ~ spl4_15
| ~ spl4_19 ),
inference(avatar_contradiction_clause,[],[f384]) ).
fof(f384,plain,
( $false
| ~ spl4_2
| ~ spl4_3
| ~ spl4_5
| ~ spl4_7
| ~ spl4_9
| ~ spl4_11
| ~ spl4_15
| ~ spl4_19 ),
inference(trivial_inequality_removal,[],[f383]) ).
fof(f383,plain,
( identity != identity
| ~ spl4_2
| ~ spl4_3
| ~ spl4_5
| ~ spl4_7
| ~ spl4_9
| ~ spl4_11
| ~ spl4_15
| ~ spl4_19 ),
inference(superposition,[],[f381,f297]) ).
fof(f381,plain,
( identity != inverse(identity)
| ~ spl4_2
| ~ spl4_3
| ~ spl4_5
| ~ spl4_7
| ~ spl4_9
| ~ spl4_11
| ~ spl4_15
| ~ spl4_19 ),
inference(trivial_inequality_removal,[],[f376]) ).
fof(f376,plain,
( identity != inverse(identity)
| identity != identity
| ~ spl4_2
| ~ spl4_3
| ~ spl4_5
| ~ spl4_7
| ~ spl4_9
| ~ spl4_11
| ~ spl4_15
| ~ spl4_19 ),
inference(superposition,[],[f375,f1]) ).
fof(f375,plain,
( ! [X5] :
( identity != multiply(X5,identity)
| identity != inverse(X5) )
| ~ spl4_2
| ~ spl4_3
| ~ spl4_5
| ~ spl4_7
| ~ spl4_9
| ~ spl4_11
| ~ spl4_15
| ~ spl4_19 ),
inference(forward_demodulation,[],[f374,f279]) ).
fof(f374,plain,
( ! [X5] :
( sk_c9 != multiply(X5,identity)
| identity != inverse(X5) )
| ~ spl4_2
| ~ spl4_3
| ~ spl4_5
| ~ spl4_7
| ~ spl4_9
| ~ spl4_11
| ~ spl4_15
| ~ spl4_19 ),
inference(forward_demodulation,[],[f373,f277]) ).
fof(f373,plain,
( ! [X5] :
( sk_c7 != inverse(X5)
| sk_c9 != multiply(X5,identity) )
| ~ spl4_2
| ~ spl4_3
| ~ spl4_5
| ~ spl4_7
| ~ spl4_9
| ~ spl4_11
| ~ spl4_15
| ~ spl4_19 ),
inference(forward_demodulation,[],[f146,f277]) ).
fof(f372,plain,
( ~ spl4_2
| ~ spl4_3
| ~ spl4_5
| ~ spl4_7
| ~ spl4_9
| ~ spl4_11
| ~ spl4_13
| ~ spl4_15 ),
inference(avatar_contradiction_clause,[],[f371]) ).
fof(f371,plain,
( $false
| ~ spl4_2
| ~ spl4_3
| ~ spl4_5
| ~ spl4_7
| ~ spl4_9
| ~ spl4_11
| ~ spl4_13
| ~ spl4_15 ),
inference(trivial_inequality_removal,[],[f370]) ).
fof(f370,plain,
( identity != identity
| ~ spl4_2
| ~ spl4_3
| ~ spl4_5
| ~ spl4_7
| ~ spl4_9
| ~ spl4_11
| ~ spl4_13
| ~ spl4_15 ),
inference(superposition,[],[f369,f1]) ).
fof(f369,plain,
( identity != multiply(identity,identity)
| ~ spl4_2
| ~ spl4_3
| ~ spl4_5
| ~ spl4_7
| ~ spl4_9
| ~ spl4_11
| ~ spl4_13
| ~ spl4_15 ),
inference(trivial_inequality_removal,[],[f368]) ).
fof(f368,plain,
( identity != multiply(identity,identity)
| identity != identity
| ~ spl4_2
| ~ spl4_3
| ~ spl4_5
| ~ spl4_7
| ~ spl4_9
| ~ spl4_11
| ~ spl4_13
| ~ spl4_15 ),
inference(forward_demodulation,[],[f363,f297]) ).
fof(f363,plain,
( identity != multiply(identity,identity)
| identity != inverse(identity)
| ~ spl4_2
| ~ spl4_3
| ~ spl4_5
| ~ spl4_7
| ~ spl4_9
| ~ spl4_11
| ~ spl4_13
| ~ spl4_15 ),
inference(superposition,[],[f359,f1]) ).
fof(f359,plain,
( ! [X4] :
( identity != multiply(identity,multiply(X4,identity))
| identity != inverse(X4) )
| ~ spl4_2
| ~ spl4_3
| ~ spl4_5
| ~ spl4_7
| ~ spl4_9
| ~ spl4_11
| ~ spl4_13
| ~ spl4_15 ),
inference(forward_demodulation,[],[f358,f283]) ).
fof(f358,plain,
( ! [X4] :
( sk_c8 != multiply(identity,multiply(X4,identity))
| identity != inverse(X4) )
| ~ spl4_2
| ~ spl4_3
| ~ spl4_5
| ~ spl4_7
| ~ spl4_9
| ~ spl4_11
| ~ spl4_13
| ~ spl4_15 ),
inference(forward_demodulation,[],[f357,f279]) ).
fof(f357,plain,
( ! [X4] :
( identity != inverse(X4)
| sk_c8 != multiply(sk_c9,multiply(X4,sk_c9)) )
| ~ spl4_2
| ~ spl4_3
| ~ spl4_5
| ~ spl4_7
| ~ spl4_9
| ~ spl4_11
| ~ spl4_13
| ~ spl4_15 ),
inference(forward_demodulation,[],[f116,f279]) ).
fof(f356,plain,
( spl4_1
| ~ spl4_2
| ~ spl4_3
| ~ spl4_5
| ~ spl4_7
| ~ spl4_9
| ~ spl4_11
| ~ spl4_15 ),
inference(avatar_contradiction_clause,[],[f355]) ).
fof(f355,plain,
( $false
| spl4_1
| ~ spl4_2
| ~ spl4_3
| ~ spl4_5
| ~ spl4_7
| ~ spl4_9
| ~ spl4_11
| ~ spl4_15 ),
inference(trivial_inequality_removal,[],[f354]) ).
fof(f354,plain,
( identity != identity
| spl4_1
| ~ spl4_2
| ~ spl4_3
| ~ spl4_5
| ~ spl4_7
| ~ spl4_9
| ~ spl4_11
| ~ spl4_15 ),
inference(superposition,[],[f281,f283]) ).
fof(f281,plain,
( identity != sk_c8
| spl4_1
| ~ spl4_2
| ~ spl4_3
| ~ spl4_5
| ~ spl4_7
| ~ spl4_9
| ~ spl4_11
| ~ spl4_15 ),
inference(backward_demodulation,[],[f234,f277]) ).
fof(f234,plain,
( sk_c7 != sk_c8
| spl4_1
| ~ spl4_2
| ~ spl4_3
| ~ spl4_5
| ~ spl4_7
| ~ spl4_9
| ~ spl4_11
| ~ spl4_15 ),
inference(backward_demodulation,[],[f217,f231]) ).
fof(f217,plain,
( sk_c8 != multiply(sk_c7,sk_c7)
| spl4_1
| ~ spl4_3
| ~ spl4_5
| ~ spl4_7
| ~ spl4_9
| ~ spl4_15 ),
inference(backward_demodulation,[],[f58,f216]) ).
fof(f58,plain,
( multiply(sk_c7,sk_c9) != sk_c8
| spl4_1 ),
inference(avatar_component_clause,[],[f57]) ).
fof(f185,plain,
( spl4_4
| spl4_15 ),
inference(avatar_split_clause,[],[f13,f125,f70]) ).
fof(f13,axiom,
( sk_c8 = inverse(sk_c4)
| sk_c8 = multiply(sk_c9,sk_c2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_10) ).
fof(f184,plain,
( spl4_4
| spl4_2 ),
inference(avatar_split_clause,[],[f17,f61,f70]) ).
fof(f17,axiom,
( sk_c9 = inverse(sk_c6)
| sk_c8 = multiply(sk_c9,sk_c2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_14) ).
fof(f183,plain,
( spl4_16
| spl4_22 ),
inference(avatar_split_clause,[],[f50,f181,f133]) ).
fof(f133,plain,
( spl4_16
<=> sP1 ),
introduced(avatar_definition,[new_symbols(naming,[spl4_16])]) ).
fof(f50,plain,
! [X6] :
( sk_c8 != inverse(X6)
| sk_c7 != multiply(X6,sk_c8)
| sP1 ),
inference(cnf_transformation,[],[f50_D]) ).
fof(f50_D,plain,
( ! [X6] :
( sk_c8 != inverse(X6)
| sk_c7 != multiply(X6,sk_c8) )
<=> ~ sP1 ),
introduced(general_splitting_component_introduction,[new_symbols(naming,[sP1])]) ).
fof(f179,plain,
( spl4_2
| spl4_14 ),
inference(avatar_split_clause,[],[f38,f121,f61]) ).
fof(f38,axiom,
( sk_c9 = multiply(sk_c3,sk_c7)
| sk_c9 = inverse(sk_c6) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_35) ).
fof(f178,plain,
( spl4_3
| spl4_8 ),
inference(avatar_split_clause,[],[f25,f89,f66]) ).
fof(f25,axiom,
( sk_c9 = inverse(sk_c1)
| sk_c7 = inverse(sk_c8) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_22) ).
fof(f177,plain,
( spl4_4
| spl4_9 ),
inference(avatar_split_clause,[],[f14,f93,f70]) ).
fof(f14,axiom,
( sk_c9 = multiply(sk_c5,sk_c8)
| sk_c8 = multiply(sk_c9,sk_c2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_11) ).
fof(f176,plain,
( spl4_9
| spl4_1 ),
inference(avatar_split_clause,[],[f7,f57,f93]) ).
fof(f7,axiom,
( multiply(sk_c7,sk_c9) = sk_c8
| sk_c9 = multiply(sk_c5,sk_c8) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_4) ).
fof(f175,plain,
( spl4_1
| spl4_11 ),
inference(avatar_split_clause,[],[f9,f106,f57]) ).
fof(f9,axiom,
( sk_c7 = multiply(sk_c6,sk_c9)
| multiply(sk_c7,sk_c9) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_6) ).
fof(f174,plain,
( spl4_6
| spl4_5 ),
inference(avatar_split_clause,[],[f40,f75,f80]) ).
fof(f40,axiom,
( sk_c7 = multiply(sk_c4,sk_c8)
| sk_c7 = inverse(sk_c3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_37) ).
fof(f173,plain,
( spl4_2
| spl4_8 ),
inference(avatar_split_clause,[],[f31,f89,f61]) ).
fof(f31,axiom,
( sk_c9 = inverse(sk_c1)
| sk_c9 = inverse(sk_c6) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_28) ).
fof(f172,plain,
( spl4_7
| spl4_8 ),
inference(avatar_split_clause,[],[f29,f89,f84]) ).
fof(f29,axiom,
( sk_c9 = inverse(sk_c1)
| sk_c8 = inverse(sk_c5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_26) ).
fof(f171,plain,
( spl4_4
| spl4_7 ),
inference(avatar_split_clause,[],[f15,f84,f70]) ).
fof(f15,axiom,
( sk_c8 = inverse(sk_c5)
| sk_c8 = multiply(sk_c9,sk_c2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_12) ).
fof(f170,plain,
( spl4_14
| spl4_3 ),
inference(avatar_split_clause,[],[f32,f66,f121]) ).
fof(f32,axiom,
( sk_c7 = inverse(sk_c8)
| sk_c9 = multiply(sk_c3,sk_c7) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_29) ).
fof(f169,plain,
( spl4_14
| spl4_11 ),
inference(avatar_split_clause,[],[f37,f106,f121]) ).
fof(f37,axiom,
( sk_c7 = multiply(sk_c6,sk_c9)
| sk_c9 = multiply(sk_c3,sk_c7) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_34) ).
fof(f168,plain,
( spl4_8
| spl4_15 ),
inference(avatar_split_clause,[],[f27,f125,f89]) ).
fof(f27,axiom,
( sk_c8 = inverse(sk_c4)
| sk_c9 = inverse(sk_c1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_24) ).
fof(f167,plain,
( spl4_14
| spl4_5 ),
inference(avatar_split_clause,[],[f33,f75,f121]) ).
fof(f33,axiom,
( sk_c7 = multiply(sk_c4,sk_c8)
| sk_c9 = multiply(sk_c3,sk_c7) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_30) ).
fof(f166,plain,
( spl4_7
| spl4_14 ),
inference(avatar_split_clause,[],[f36,f121,f84]) ).
fof(f36,axiom,
( sk_c9 = multiply(sk_c3,sk_c7)
| sk_c8 = inverse(sk_c5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_33) ).
fof(f165,plain,
( spl4_10
| spl4_3 ),
inference(avatar_split_clause,[],[f18,f66,f101]) ).
fof(f18,axiom,
( sk_c7 = inverse(sk_c8)
| sk_c2 = multiply(sk_c1,sk_c9) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_15) ).
fof(f164,plain,
( spl4_5
| spl4_1 ),
inference(avatar_split_clause,[],[f5,f57,f75]) ).
fof(f5,axiom,
( multiply(sk_c7,sk_c9) = sk_c8
| sk_c7 = multiply(sk_c4,sk_c8) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_2) ).
fof(f163,plain,
( spl4_11
| spl4_4 ),
inference(avatar_split_clause,[],[f16,f70,f106]) ).
fof(f16,axiom,
( sk_c8 = multiply(sk_c9,sk_c2)
| sk_c7 = multiply(sk_c6,sk_c9) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_13) ).
fof(f162,plain,
( spl4_10
| spl4_5 ),
inference(avatar_split_clause,[],[f19,f75,f101]) ).
fof(f19,axiom,
( sk_c7 = multiply(sk_c4,sk_c8)
| sk_c2 = multiply(sk_c1,sk_c9) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_16) ).
fof(f161,plain,
( spl4_6
| spl4_15 ),
inference(avatar_split_clause,[],[f41,f125,f80]) ).
fof(f41,axiom,
( sk_c8 = inverse(sk_c4)
| sk_c7 = inverse(sk_c3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_38) ).
fof(f160,plain,
( spl4_6
| spl4_3 ),
inference(avatar_split_clause,[],[f39,f66,f80]) ).
fof(f39,axiom,
( sk_c7 = inverse(sk_c8)
| sk_c7 = inverse(sk_c3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_36) ).
fof(f159,plain,
( spl4_10
| spl4_7 ),
inference(avatar_split_clause,[],[f22,f84,f101]) ).
fof(f22,axiom,
( sk_c8 = inverse(sk_c5)
| sk_c2 = multiply(sk_c1,sk_c9) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_19) ).
fof(f158,plain,
( spl4_10
| spl4_11 ),
inference(avatar_split_clause,[],[f23,f106,f101]) ).
fof(f23,axiom,
( sk_c7 = multiply(sk_c6,sk_c9)
| sk_c2 = multiply(sk_c1,sk_c9) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_20) ).
fof(f157,plain,
( spl4_21
| spl4_18 ),
inference(avatar_split_clause,[],[f52,f141,f155]) ).
fof(f141,plain,
( spl4_18
<=> sP2 ),
introduced(avatar_definition,[new_symbols(naming,[spl4_18])]) ).
fof(f52,plain,
! [X7] :
( sP2
| sk_c9 != multiply(X7,sk_c8)
| sk_c8 != inverse(X7) ),
inference(cnf_transformation,[],[f52_D]) ).
fof(f52_D,plain,
( ! [X7] :
( sk_c9 != multiply(X7,sk_c8)
| sk_c8 != inverse(X7) )
<=> ~ sP2 ),
introduced(general_splitting_component_introduction,[new_symbols(naming,[sP2])]) ).
fof(f153,plain,
( spl4_15
| spl4_10 ),
inference(avatar_split_clause,[],[f20,f101,f125]) ).
fof(f20,axiom,
( sk_c2 = multiply(sk_c1,sk_c9)
| sk_c8 = inverse(sk_c4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_17) ).
fof(f152,plain,
( spl4_17
| spl4_20 ),
inference(avatar_split_clause,[],[f48,f150,f137]) ).
fof(f137,plain,
( spl4_17
<=> sP0 ),
introduced(avatar_definition,[new_symbols(naming,[spl4_17])]) ).
fof(f48,plain,
! [X8] :
( sk_c9 != inverse(X8)
| sP0
| sk_c7 != multiply(X8,sk_c9) ),
inference(cnf_transformation,[],[f48_D]) ).
fof(f48_D,plain,
( ! [X8] :
( sk_c9 != inverse(X8)
| sk_c7 != multiply(X8,sk_c9) )
<=> ~ sP0 ),
introduced(general_splitting_component_introduction,[new_symbols(naming,[sP0])]) ).
fof(f148,plain,
( spl4_1
| spl4_15 ),
inference(avatar_split_clause,[],[f6,f125,f57]) ).
fof(f6,axiom,
( sk_c8 = inverse(sk_c4)
| multiply(sk_c7,sk_c9) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_3) ).
fof(f147,plain,
( ~ spl4_12
| ~ spl4_16
| ~ spl4_17
| ~ spl4_1
| ~ spl4_18
| spl4_19
| ~ spl4_3 ),
inference(avatar_split_clause,[],[f55,f66,f145,f141,f57,f137,f133,f111]) ).
fof(f111,plain,
( spl4_12
<=> sP3 ),
introduced(avatar_definition,[new_symbols(naming,[spl4_12])]) ).
fof(f55,plain,
! [X5] :
( sk_c7 != inverse(sk_c8)
| sk_c9 != multiply(X5,sk_c7)
| ~ sP2
| sk_c7 != inverse(X5)
| multiply(sk_c7,sk_c9) != sk_c8
| ~ sP0
| ~ sP1
| ~ sP3 ),
inference(general_splitting,[],[f53,f54_D]) ).
fof(f54,plain,
! [X4] :
( sk_c9 != inverse(X4)
| sk_c8 != multiply(sk_c9,multiply(X4,sk_c9))
| sP3 ),
inference(cnf_transformation,[],[f54_D]) ).
fof(f54_D,plain,
( ! [X4] :
( sk_c9 != inverse(X4)
| sk_c8 != multiply(sk_c9,multiply(X4,sk_c9)) )
<=> ~ sP3 ),
introduced(general_splitting_component_introduction,[new_symbols(naming,[sP3])]) ).
fof(f53,plain,
! [X4,X5] :
( sk_c8 != multiply(sk_c9,multiply(X4,sk_c9))
| sk_c9 != inverse(X4)
| sk_c7 != inverse(X5)
| sk_c9 != multiply(X5,sk_c7)
| sk_c7 != inverse(sk_c8)
| multiply(sk_c7,sk_c9) != sk_c8
| ~ sP0
| ~ sP1
| ~ sP2 ),
inference(general_splitting,[],[f51,f52_D]) ).
fof(f51,plain,
! [X7,X4,X5] :
( sk_c9 != multiply(X7,sk_c8)
| sk_c8 != inverse(X7)
| sk_c8 != multiply(sk_c9,multiply(X4,sk_c9))
| sk_c9 != inverse(X4)
| sk_c7 != inverse(X5)
| sk_c9 != multiply(X5,sk_c7)
| sk_c7 != inverse(sk_c8)
| multiply(sk_c7,sk_c9) != sk_c8
| ~ sP0
| ~ sP1 ),
inference(general_splitting,[],[f49,f50_D]) ).
fof(f49,plain,
! [X6,X7,X4,X5] :
( sk_c9 != multiply(X7,sk_c8)
| sk_c8 != inverse(X7)
| sk_c8 != multiply(sk_c9,multiply(X4,sk_c9))
| sk_c9 != inverse(X4)
| sk_c7 != inverse(X5)
| sk_c7 != multiply(X6,sk_c8)
| sk_c9 != multiply(X5,sk_c7)
| sk_c8 != inverse(X6)
| sk_c7 != inverse(sk_c8)
| multiply(sk_c7,sk_c9) != sk_c8
| ~ sP0 ),
inference(general_splitting,[],[f47,f48_D]) ).
fof(f47,plain,
! [X8,X6,X7,X4,X5] :
( sk_c9 != multiply(X7,sk_c8)
| sk_c8 != inverse(X7)
| sk_c7 != multiply(X8,sk_c9)
| sk_c8 != multiply(sk_c9,multiply(X4,sk_c9))
| sk_c9 != inverse(X4)
| sk_c7 != inverse(X5)
| sk_c7 != multiply(X6,sk_c8)
| sk_c9 != inverse(X8)
| sk_c9 != multiply(X5,sk_c7)
| sk_c8 != inverse(X6)
| sk_c7 != inverse(sk_c8)
| multiply(sk_c7,sk_c9) != sk_c8 ),
inference(equality_resolution,[],[f46]) ).
fof(f46,axiom,
! [X3,X8,X6,X7,X4,X5] :
( sk_c9 != multiply(X7,sk_c8)
| sk_c8 != inverse(X7)
| sk_c7 != multiply(X8,sk_c9)
| sk_c8 != multiply(sk_c9,X3)
| sk_c9 != inverse(X4)
| sk_c7 != inverse(X5)
| multiply(X4,sk_c9) != X3
| sk_c7 != multiply(X6,sk_c8)
| sk_c9 != inverse(X8)
| sk_c9 != multiply(X5,sk_c7)
| sk_c8 != inverse(X6)
| sk_c7 != inverse(sk_c8)
| multiply(sk_c7,sk_c9) != sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_43) ).
fof(f131,plain,
( spl4_1
| spl4_7 ),
inference(avatar_split_clause,[],[f8,f84,f57]) ).
fof(f8,axiom,
( sk_c8 = inverse(sk_c5)
| multiply(sk_c7,sk_c9) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_5) ).
fof(f130,plain,
( spl4_10
| spl4_9 ),
inference(avatar_split_clause,[],[f21,f93,f101]) ).
fof(f21,axiom,
( sk_c9 = multiply(sk_c5,sk_c8)
| sk_c2 = multiply(sk_c1,sk_c9) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_18) ).
fof(f129,plain,
( spl4_9
| spl4_14 ),
inference(avatar_split_clause,[],[f35,f121,f93]) ).
fof(f35,axiom,
( sk_c9 = multiply(sk_c3,sk_c7)
| sk_c9 = multiply(sk_c5,sk_c8) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_32) ).
fof(f128,plain,
( spl4_14
| spl4_15 ),
inference(avatar_split_clause,[],[f34,f125,f121]) ).
fof(f34,axiom,
( sk_c8 = inverse(sk_c4)
| sk_c9 = multiply(sk_c3,sk_c7) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_31) ).
fof(f119,plain,
( spl4_11
| spl4_8 ),
inference(avatar_split_clause,[],[f30,f89,f106]) ).
fof(f30,axiom,
( sk_c9 = inverse(sk_c1)
| sk_c7 = multiply(sk_c6,sk_c9) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_27) ).
fof(f118,plain,
( spl4_3
| spl4_1 ),
inference(avatar_split_clause,[],[f4,f57,f66]) ).
fof(f4,axiom,
( multiply(sk_c7,sk_c9) = sk_c8
| sk_c7 = inverse(sk_c8) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_1) ).
fof(f117,plain,
( spl4_12
| spl4_13 ),
inference(avatar_split_clause,[],[f54,f115,f111]) ).
fof(f109,plain,
( spl4_6
| spl4_11 ),
inference(avatar_split_clause,[],[f44,f106,f80]) ).
fof(f44,axiom,
( sk_c7 = multiply(sk_c6,sk_c9)
| sk_c7 = inverse(sk_c3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_41) ).
fof(f104,plain,
( spl4_2
| spl4_10 ),
inference(avatar_split_clause,[],[f24,f101,f61]) ).
fof(f24,axiom,
( sk_c2 = multiply(sk_c1,sk_c9)
| sk_c9 = inverse(sk_c6) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_21) ).
fof(f99,plain,
( spl4_9
| spl4_6 ),
inference(avatar_split_clause,[],[f42,f80,f93]) ).
fof(f42,axiom,
( sk_c7 = inverse(sk_c3)
| sk_c9 = multiply(sk_c5,sk_c8) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_39) ).
fof(f98,plain,
( spl4_6
| spl4_2 ),
inference(avatar_split_clause,[],[f45,f61,f80]) ).
fof(f45,axiom,
( sk_c9 = inverse(sk_c6)
| sk_c7 = inverse(sk_c3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_42) ).
fof(f97,plain,
( spl4_5
| spl4_8 ),
inference(avatar_split_clause,[],[f26,f89,f75]) ).
fof(f26,axiom,
( sk_c9 = inverse(sk_c1)
| sk_c7 = multiply(sk_c4,sk_c8) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_23) ).
fof(f96,plain,
( spl4_8
| spl4_9 ),
inference(avatar_split_clause,[],[f28,f93,f89]) ).
fof(f28,axiom,
( sk_c9 = multiply(sk_c5,sk_c8)
| sk_c9 = inverse(sk_c1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_25) ).
fof(f87,plain,
( spl4_6
| spl4_7 ),
inference(avatar_split_clause,[],[f43,f84,f80]) ).
fof(f43,axiom,
( sk_c8 = inverse(sk_c5)
| sk_c7 = inverse(sk_c3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_40) ).
fof(f78,plain,
( spl4_4
| spl4_5 ),
inference(avatar_split_clause,[],[f12,f75,f70]) ).
fof(f12,axiom,
( sk_c7 = multiply(sk_c4,sk_c8)
| sk_c8 = multiply(sk_c9,sk_c2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_9) ).
fof(f73,plain,
( spl4_3
| spl4_4 ),
inference(avatar_split_clause,[],[f11,f70,f66]) ).
fof(f11,axiom,
( sk_c8 = multiply(sk_c9,sk_c2)
| sk_c7 = inverse(sk_c8) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_8) ).
fof(f64,plain,
( spl4_1
| spl4_2 ),
inference(avatar_split_clause,[],[f10,f61,f57]) ).
fof(f10,axiom,
( sk_c9 = inverse(sk_c6)
| multiply(sk_c7,sk_c9) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_7) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP369-1 : TPTP v8.1.0. Released v2.5.0.
% 0.07/0.13 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% 0.12/0.33 % Computer : n008.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Mon Aug 29 22:30:25 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.18/0.49 % (32640)fmb+10_1:1_bce=on:fmbsr=1.5:nm=4:skr=on:i=191324:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/191324Mi)
% 0.18/0.50 % (32662)dis+21_1:1_av=off:er=filter:slsq=on:slsqc=0:slsqr=1,1:sp=frequency:to=lpo:i=498:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/498Mi)
% 0.18/0.50 % (32654)ins+10_1:1_awrs=decay:awrsf=30:bsr=unit_only:foolp=on:igrr=8/457:igs=10:igwr=on:nwc=1.5:sp=weighted_frequency:to=lpo:uhcvi=on:i=68:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/68Mi)
% 0.18/0.50 % (32649)ott-1_1:6_av=off:cond=on:fsr=off:nwc=3.0:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.18/0.50 % (32659)ott+4_1:1_av=off:bd=off:nwc=5.0:rp=on:s2a=on:s2at=2.0:slsq=on:slsqc=2:slsql=off:slsqr=1,2:sp=frequency:i=100:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/100Mi)
% 0.18/0.51 % (32650)ott+2_1:1_fsr=off:gsp=on:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 0.18/0.51 % (32651)ott+10_1:32_bd=off:fsr=off:newcnf=on:tgt=full:i=100:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/100Mi)
% 0.18/0.51 TRYING [1]
% 0.18/0.51 % (32667)ins+10_1:1_awrs=decay:awrsf=30:bsr=unit_only:foolp=on:igrr=8/457:igs=10:igwr=on:nwc=1.5:sp=weighted_frequency:to=lpo:uhcvi=on:i=68:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/68Mi)
% 0.18/0.51 % (32642)ott+4_1:1_av=off:bd=off:nwc=5.0:s2a=on:s2at=2.0:slsq=on:slsqc=2:slsql=off:slsqr=1,2:sp=frequency:i=37:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/37Mi)
% 0.18/0.52 % (32653)ott+10_1:5_bd=off:tgt=full:i=99:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99Mi)
% 0.18/0.52 % (32644)ott+33_1:4_s2a=on:tgt=ground:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.18/0.52 % (32664)ott+10_1:1_kws=precedence:tgt=ground:i=482:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/482Mi)
% 0.18/0.52 % (32643)ott+10_1:32_bd=off:fsr=off:newcnf=on:tgt=full:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.18/0.52 % (32641)ott+10_1:32_abs=on:br=off:urr=ec_only:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 0.18/0.52 % (32648)dis+2_1:64_add=large:bce=on:bd=off:i=2:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.18/0.52 % (32648)Instruction limit reached!
% 0.18/0.52 % (32648)------------------------------
% 0.18/0.52 % (32648)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.18/0.52 % (32648)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.18/0.52 % (32648)Termination reason: Unknown
% 0.18/0.52 % (32648)Termination phase: Saturation
% 0.18/0.52
% 0.18/0.52 % (32648)Memory used [KB]: 895
% 0.18/0.52 % (32648)Time elapsed: 0.003 s
% 0.18/0.52 % (32648)Instructions burned: 2 (million)
% 0.18/0.52 % (32648)------------------------------
% 0.18/0.52 % (32648)------------------------------
% 1.44/0.52 % (32668)ott+11_2:3_av=off:fde=unused:nwc=5.0:tgt=ground:i=177:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/177Mi)
% 1.44/0.52 % (32660)ott+10_1:8_bsd=on:fsd=on:lcm=predicate:nwc=5.0:s2a=on:s2at=1.5:spb=goal_then_units:i=176:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/176Mi)
% 1.44/0.53 % (32663)ott+11_1:1_drc=off:nwc=5.0:slsq=on:slsqc=1:spb=goal_then_units:to=lpo:i=467:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/467Mi)
% 1.44/0.53 TRYING [2]
% 1.44/0.53 % (32670)ott+10_7:2_awrs=decay:awrsf=8:bd=preordered:drc=off:fd=preordered:fde=unused:fsr=off:slsq=on:slsqc=2:slsqr=5,8:sp=const_min:spb=units:to=lpo:i=355:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/355Mi)
% 1.44/0.53 TRYING [3]
% 1.44/0.53 % (32656)dis+34_1:32_abs=on:add=off:bsr=on:gsp=on:sp=weighted_frequency:i=99:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99Mi)
% 1.44/0.53 % (32666)ott+10_1:5_bd=off:tgt=full:i=500:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/500Mi)
% 1.44/0.53 % (32645)dis+34_1:32_abs=on:add=off:bsr=on:gsp=on:sp=weighted_frequency:i=48:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/48Mi)
% 1.44/0.53 % (32652)ott+10_1:28_bd=off:bs=on:tgt=ground:i=101:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/101Mi)
% 1.44/0.53 % (32658)ott+10_1:1_tgt=ground:i=100:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/100Mi)
% 1.44/0.53 % (32655)ott+11_2:3_av=off:fde=unused:nwc=5.0:tgt=ground:i=75:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/75Mi)
% 1.44/0.53 % (32657)fmb+10_1:1_bce=on:i=59:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/59Mi)
% 1.44/0.54 % (32647)dis+10_1:1_fsd=on:sp=occurrence:i=7:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 1.44/0.54 % (32669)ott+33_1:4_s2a=on:tgt=ground:i=439:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/439Mi)
% 1.44/0.54 TRYING [1]
% 1.44/0.54 % (32646)fmb+10_1:1_fmbsr=2.0:nm=4:skr=on:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 1.44/0.54 TRYING [2]
% 1.44/0.54 % (32647)Instruction limit reached!
% 1.44/0.54 % (32647)------------------------------
% 1.44/0.54 % (32647)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.44/0.54 % (32647)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.44/0.54 % (32647)Termination reason: Unknown
% 1.44/0.54 % (32647)Termination phase: Saturation
% 1.44/0.54
% 1.44/0.54 % (32647)Memory used [KB]: 5628
% 1.44/0.54 % (32647)Time elapsed: 0.152 s
% 1.44/0.54 % (32647)Instructions burned: 9 (million)
% 1.44/0.54 % (32647)------------------------------
% 1.44/0.54 % (32647)------------------------------
% 1.44/0.54 TRYING [3]
% 1.55/0.54 TRYING [1]
% 1.55/0.54 TRYING [2]
% 1.55/0.55 % (32661)ott+3_1:1_gsp=on:lcm=predicate:i=138:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/138Mi)
% 1.55/0.55 TRYING [4]
% 1.55/0.56 % (32650)First to succeed.
% 1.55/0.56 TRYING [3]
% 1.55/0.57 TRYING [4]
% 1.55/0.57 TRYING [4]
% 1.55/0.57 % (32642)Instruction limit reached!
% 1.55/0.57 % (32642)------------------------------
% 1.55/0.57 % (32642)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.55/0.57 % (32642)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.55/0.57 % (32642)Termination reason: Unknown
% 1.55/0.57 % (32642)Termination phase: Saturation
% 1.55/0.57
% 1.55/0.57 % (32642)Memory used [KB]: 1151
% 1.55/0.57 % (32642)Time elapsed: 0.165 s
% 1.55/0.57 % (32642)Instructions burned: 38 (million)
% 1.55/0.57 % (32642)------------------------------
% 1.55/0.57 % (32642)------------------------------
% 1.55/0.58 % (32649)Instruction limit reached!
% 1.55/0.58 % (32649)------------------------------
% 1.55/0.58 % (32649)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.55/0.58 % (32649)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.55/0.58 % (32649)Termination reason: Unknown
% 1.55/0.58 % (32649)Termination phase: Saturation
% 1.55/0.58
% 1.55/0.58 % (32649)Memory used [KB]: 1407
% 1.55/0.58 % (32649)Time elapsed: 0.192 s
% 1.55/0.58 % (32649)Instructions burned: 51 (million)
% 1.55/0.58 % (32649)------------------------------
% 1.55/0.58 % (32649)------------------------------
% 1.55/0.59 % (32650)Refutation found. Thanks to Tanya!
% 1.55/0.59 % SZS status Unsatisfiable for theBenchmark
% 1.55/0.59 % SZS output start Proof for theBenchmark
% See solution above
% 1.55/0.60 % (32650)------------------------------
% 1.55/0.60 % (32650)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.55/0.60 % (32650)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.55/0.60 % (32650)Termination reason: Refutation
% 1.55/0.60
% 1.55/0.60 % (32650)Memory used [KB]: 6012
% 1.55/0.60 % (32650)Time elapsed: 0.164 s
% 1.55/0.60 % (32650)Instructions burned: 31 (million)
% 1.55/0.60 % (32650)------------------------------
% 1.55/0.60 % (32650)------------------------------
% 1.55/0.60 % (32639)Success in time 0.248 s
%------------------------------------------------------------------------------